2008/12/28 by Guy Roos, Roos, Guy
Mathematics · #17C40 #30B10 #32A05 #32M15 #Advanced Banach Space Theory #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:17C40 #msc:30B10 #msc:32A05 #msc:32M15
paper · pdf · doi:10.48550/arxiv.0812.4815
15 pages Version 2. References added. Section 1.2 has been rewritten and improved. Section 2.4 on open problems has been corrected and precised
openalex publication_date 2008/12/28 · arxiv created 2009/04/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theorem of Harald Bohr (1914) states that if f is a holomorphic map from the unit disc into itself, then the sum of absolute values of its Taylor expansion is less than 1 for |z|<1/3. The bound 1/3 is optimal. This result has been extended in a suitable sense by Liu Taishun and Wang Jianfei (2007) to the bounded complex symmetric domains of the four classical series, and to polydiscs. The result of Liu and Wang may be generalized to all bounded symmetric domains, with a proof which does not depend on classification.